The word 'children' doesn't only refer to little kids. In the context of family relationships, the word 'children' is a non-gender specific term covering people of any age. For example, if you are asking about a lady of 95 years old, you might say 'Does she have any children?'. Obviously, these 'children' are going to be fairly old people themselves, but that is the word we use. It might seem strange if you've only heard 'children' as a word referring to kiddies, but that is the English equivalent of 'filhos' (sons and/or daughters). There are other words (such as descendants, progeny, offspring etc) but they are not used in everyday contexts. Sorry - 'children' is the only word we have.
Your second question is easier. Yes, a 'spouse' is gender neutral - a husband or wife. It only tends to be used in legal and formal contexts, though. It isn't really an everyday term. The word 'partner' (which also covers a person - of either sex - who you may not be officially married to) is more usual nowadays.